Is it possible to have custom GROUP BY for MySQL query?

Question

I have been trying to find the simplest way to group the two age groups in my query. Is it possible for something like this to work?

SELECT age,
sum(case when age < '20' then 1 else 0 end),
sum(case when age > '20' then 1 else 0 end)
FROM Contact
GROUP BY ...."custom group one"......"custom group one".....??

I know you should group on a column usually, but in my case I that doesn't work. Any suggestions? Thx!

Table:            Desired Query Result:
Name    Age       0           1
John    18        Under 20    2
Harry   22        Over 20     2
Mary    17
Megan   27

---

SOLVED:

SELECT CASE
  WHEN age = '21' THEN 'young'
  WHEN  age BETWEEN '22' AND '60' THEN 'middle'                          
  ELSE 'old'
END, Count(id)
FROM  Contact
GROUP BY CASE
  WHEN age = '21' THEN 'young'
  WHEN  age BETWEEN '22' AND '60' THEN 'middle'                       
  ELSE 'old'
END

Note: AS can be used to assign alias to grouping conditions in SELECT statement and hence avoid repeating conditions twice, i.e.

SELECT CASE
  WHEN age = '21' THEN 'young'
  WHEN  age BETWEEN '22' AND '60' THEN 'middle'                          
  ELSE 'old'
END AS age_range, Count(id)
FROM  Contact
GROUP BY age_range

Answer 1

So that will be:

SELECT 
  COUNT(1), 
  age>20 AS Above20 
FROM t 
GROUP BY age>20

-check this fiddle.

Or, alternatively, with SUM() and with column view:

SELECT
  SUM(IF(age>20, 1, 0)) AS Above20,
  SUM(IF(age<=20, 1, 0)) AS Below20
FROM 
  t

-check this fiddle.